Steps for solving $6x - 18 = 54$ are shown. Explain how Step 1 helps solve the equation.
$6x - 18 = 54$ Original equation
$6x - 18 + 18 = 54 + 18$ Step 1
$6x = 72$ Step 2
$\frac{6x}{6} = \frac{72}{6}$ Step 3
$x = 12$ Step 4
A. Adding 18 to both sides isolates the variable.
B. Subtracting 18 from both sides combines like terms.
C. Adding 18 to both sides isolates the variable term.
D. Subtracting 18 from both sides undoes the subtraction.
Answer (2)
Adding 18 to both sides of the equation 6 x − 18 = 54 .
This eliminates the constant term on the left side, resulting in 6 x = 72 .
The variable term 6 x is now isolated.
Therefore, adding 18 to both sides isolates the variable term, and the answer is C .
Explanation
Analyzing the Original Equation and Step 1 The original equation is 6 x − 18 = 54 . We want to explain how Step 1, which is 6 x − 18 + 18 = 54 + 18 , helps solve the equation.
Effect of Adding 18 to Both Sides In Step 1, we add 18 to both sides of the original equation. Adding the same value to both sides maintains the equality. The purpose of adding 18 is to eliminate the constant term on the left side of the equation.
Isolating the Variable Term By adding 18 to both sides, we get 6 x − 18 + 18 = 54 + 18 , which simplifies to 6 x = 72 . This means that the term − 18 is eliminated from the left side, leaving only the term with the variable, 6 x . Therefore, adding 18 to both sides isolates the variable term.
Selecting the Correct Option Now, let's consider the given options:
A. Adding 18 to both sides isolates the variable. This is not entirely correct because we isolate the term 6 x , not just x .
B. Subtracting 18 from both sides combines like terms. This is incorrect because we are adding 18, not subtracting. C. Adding 18 to both sides isolates the variable term. This is the correct option because we isolate 6 x .
D. Subtracting 18 from both sides undoes the subtraction. This is incorrect because we are adding 18, not subtracting.
Final Answer Therefore, the correct answer is C. Adding 18 to both sides isolates the variable term.
Examples
When solving equations, we often use inverse operations to isolate the variable. For example, if you are saving money and have already saved 6 x − 18 dollars, and you need to reach a goal of 54 dollars, adding 18 to both sides of the equation helps you determine how much more you need to save in total ( 6 x dollars). This technique is useful in budgeting and financial planning.
Step 1 helps solve the equation by adding 18 to both sides, which eliminates the constant term on the left side of the equation. This operation effectively isolates the variable term, resulting in a simplified equation. Therefore, the correct answer is C.
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